Spatial transcriptomics measures gene expression while preserving where in the tissue each measurement came from. But real experiments produce multiple tissue slices, each with different spatial dimensions, different technical biases, and different mixtures of cell types in each spot. The slices don't align neatly. Comparing them requires solving three entangled problems: batch correction (removing technical variation), deconvolution (unmixing cell types within each spatial unit), and imputation (filling in genes that one platform measured and another didn't).
Cottrell, Wei, and Huang (arXiv:2603.22477) solve all three with a single tensor decomposition. STORM — Subspace Tensor Orthogonal Rotation Model — treats each tissue slice as a matrix of genes by spatial locations, stacks the slices into a tensor, and factorizes the tensor into shared latent factors that capture the microenvironmental patterns common across slices. The orthogonal rotation ensures the factors are interpretable — each corresponds to a distinct tissue pattern rather than an arbitrary mixture.
The key move is treating the spatial dimension as informative structure rather than nuisance variation. Standard batch correction methods align distributions across samples by removing differences. STORM aligns the microenvironmental patterns — the spatial organization of cell types and expression programs — and lets the remaining differences be biological. The spatial context is what makes the alignment meaningful: two spots that share a microenvironmental pattern across slices should be aligned even if their raw expression profiles differ due to batch effects.
The tensor factorization handles the three problems simultaneously because they share the same latent structure. The factors that align batches are the same factors that identify cell-type mixtures and predict missing genes. One decomposition, three applications. The problems were never really separate.